Study of shock non-stationarity with 1-D and 2-D hybrid simulations

Xingqiu Yuan, Iver Cairns, School of Physics, University of Sydney, NSW, Australia

Larisa TrichtchenkoGeomagnetic Lab., Natural Resource Canada, ON, Canada

Robert RankinDept of Physics, University of Alberta, Edmonton, AB, Canada

STEREO SWG 21/4/08

Outline

Controversy: Do shocks reform in > 1D?

1. Observational evidence2. Previous simulations3. Simulation code4. Demonstrations that shocks reform in > 1 D5. Wave spectra6. Summary & implications for STEREO

1. Observational evidence that shocks reform

Low frequency oscillations of the ion flux in shocks observed [Vaisberg et al., 1984; Bagenal

et al., 1987].

Strong support claimed for shock reformation recently [Horbury et al., 2001; Lobzin et al., 2007].

But, all indirect.

2. Theory & simulations: Steady- state or Reforming?

1-D hybrid/PIC simulations fronts of perpendicular & quasi-perp shocks vary with time and reform [Leroy

et al., 1982; Quest, 1986; Hellinger, 2002; Scholer 2003; Yuan et al., 2007]. 2-D PIC simulations reformation for high MA q-

perp shocks [Lembege and Dawson, 1987; Lembege and Savoini,

1992]. Whistler-breaking theory q-perp shocks unsteady

at high enough MA [Krasnoselskikh et al., 2002]

However, recent 2D PIC/hybrid simulation analysis claims shock reformation stops because of large amplitude whistler waves [Hellinger et al., 2007]

Controversy: are shocks steady or reforming in 2D?

3. Hybrid Simulation code

1D3V and 2D3V parallel hybrid codes were developed: kinetic ions, massless fluid electrons.

Darwin approximation for EM waves. Injection method to generate the shocks. Predictor-corrector method to advance ions. Less diffusive algorithim. The Fortran 90 code parallelized using 1D

domain decomposition with MPI library.

4. Shock reformation in 2D

1. Recovery of Hellinger et al. [2007] results at low MA and high θbn .

2. Reformation shown at higher MA.

3. Significant wave activity.4. Reformation slows in 2D and as

MA

4.1. Recovery of Hellinger et al. at low MA

[Hellinger et al., GRL, 2007; θbn = 90]

Our results: θbn = 90 & 85.

• In 1-D find clear self-reformation for these parameters. • 2-D: confirm quasi-stationary shock front with whistlers. • But note almost periodic ripples / spatial inhomogeneities near threshold for self-reformation.

obn

e

i

AM

85&90

5.0

2.0

6.3

4.2. Clear evidence for 2D reformation

obn

e

i

AM

85

2.0

15.0

2.6

4.3 1D & 2D reforming shocks

1D hybrid: reforming shock with period about 1.6 upstream Ωci

-1

2D hybrid: reforming shock with periodabout 2.1 Ωci

-1 (upstream)

obn

e

i

AM

85

2.0

15.0

2.6

Shock reformation processes clearly observed in 1D & 2D hybrid simulations Reforming Shocks in 2D !!

4.4 Different waves in 1D and 2D

1D snapshots after 6.0 Ωci-1

No waves in the foot region

2D snapshots after 3.0 Ωci-1

• Whistler waves • ≈ 5 Ωci

, λ ≈ 0.2VA/ Ωci.

40 200100

Ex

Ey

Ez

Phi

Frequencies in simulation frame

Wave spectra

[Hellinger et al., GRL, 2007]

• FFT in y-direction, wavelet transform in x for <y> quantities. • Similar wave spectra despite “stationary” vs reforming.• ≈ consistent if “stationary” case is near reformation threshold

Whistlers with ≈ 5 Ωci in simulation frame & λ ≈ 0.2VA/ Ωci

Our results

4.5 Slower reformation in 2D

3 5

3

1

T Ωci

MA

1D

2D

obn

e

i

85

2.0

15.0

Resolved controversy: in general, shocks undergo self-reformation in 2D for high enough MA and θbn .

Hellinger et al. case verified to be time-steady but near threshold (MA , θbn , β) for reformation.

Shock reformation period increases in 2D as MA . Whistlers generated in foot in 2D, not 1D.

Could STEREO test reformation via whistlers/waves?

Extensive parameter search & understanding of role of whistlers in shock reformation needed.

5. Summary and implications for STEREO

4.5 Wave spectra

FFT transform in y-direction

Wavelet transfrom in x-direction+ y-direction average

Hellinger et al., GRL, 2007

Similar wave spectrumbut different shock Parameters and shock reformation processes

What is collisionless shock?

The collisionless shock is the nonlinear wave where the solar wind plasma can be heated and decelerated.

The dissipation processes at the shock depend on the properties of a collisionless plasma, and lead to a rich range of energetic particles and plasma waves.

Observations of the collisionless shock show a rich source of waves and energetic particles.

Shock accelerated electrons are mainly responsible for Type II/III radio emissions.